Topological magnons arise in 2D ferromagnets on honeycomb lattices with Dzyaloshinskii-Moriya Interaction (DMI). The DMI breaks time-reversal symmetry and opens a topological gap in the magnon band structure. The Chern number C = (1/2π)∫BZ Ω_k d²k (integrated Berry curvature) is a topological invariant: |C|=1 signals chiral edge states immune to backscattering. Analogous to the quantum Hall effect for electrons, but for charge-neutral spin waves.